On functions with weak iterative roots
The author, after giving the notion of weak iterative root introduced by Gy. Targonski, proves the following: Theorem: Let \(X\) be an arbitrary set. If \(f\in X^X\) has a weak iterative root of order \(r\) then it also has an iterative root of the same order. From the proof of the theorem it is seen that every weak iterative root generates a family of iterative roots.
scientific article; zbMATH DE number 1742889